Question

How do you find the solution to `cottheta-6=2cottheta+2` if `0<=theta<2pi`?

Answer 1

`-7^@125, 172^@875`

Explanation:

cot t - 6 = 2cot t + 2
- 6 - 2 = 2cot t - cot t
cot = - 8 --> `tan t = 1/(cot) = - 1/8`
Use calculator and unit circle:
`tan t = - 1/8` --> `t = -7^@125`
Trig unit circle gives another arc t that has the same tan value:
`t = - 7.125 + 180 = 172^@875`